Solve for $x$ and $y$ using elimination. ${-x-6y = -53}$ ${x-5y = -35}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-11y = -88$ $\dfrac{-11y}{{-11}} = \dfrac{-88}{{-11}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-x-6y = -53}\thinspace$ to find $x$ ${-x - 6}{(8)}{= -53}$ $-x-48 = -53$ $-x-48{+48} = -53{+48}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 8}$ into $\thinspace {x-5y = -35}\thinspace$ and get the same answer for $x$ : ${x - 5}{(8)}{= -35}$ ${x = 5}$